The present invention relates to adaptive process controllers. In particular, the present invention relates to a method and apparatus for automatically determining the ultimate gain and ultimate period of a controlled process, without significantly affecting the quality of process control.
Proportional, integral, and derivative (PID) controllers are widely used to control industrial processes. As used herein, the term PID controller encompasses all variations and combinations of the control functions of a PID controller, including P, PI, PD, and PID configurations. Such controllers are comprised of a proportional amplification unit with a proportional gain parameter K.sub.C, an integration unit with an integration time parameter T.sub.I, and a derivative unit with a derivative time parameter T.sub.D. All controller parameters must be tuned for the controller to operate effectively.
Several manual methods of tuning a PID controller, such as the Ziegler-Nichols method, are known in the prior art. To tune a PID controller according to the Ziegler-Nichols method, the integration and derivative units are disabled and an operator manually increases the proportional gain of the amplification unit until the system begins to oscillate. The proportional gain that causes the system to begin to oscillate is the ultimate gain and the reciprocal of the frequency of the process output signal y measured at this proportional gain is the ultimate period. Accordingly, the ultimate period (T.sub.U) is the period at which a process exhibits a phase lag of -180.degree.. The ultimate gain (K.sub.U) is the reciprocal of the process gain A of the process at the ultimate period. The ultimate frequency (.omega..sub.U), is related to the ultimate period by the equation: EQU T.sub.U =2 .pi./.omega..sub.U .
The parameters of the PID controller are calculated from the ultimate gain and the ultimate period by applying Ziegler-Nichols rules. For example:
K.sub.C =0.6 K.sub.U, PA1 T.sub.I =0.5 T.sub.U, and PA1 T.sub.D 0.125 T.sub.U.
While manual tuning of PID controllers is possible, it is often tedious and inaccurate, especially when characteristics of the controlled process change over time. In addition, process non-linearities, such as dead zone time and hysteresis, may make it difficult to bring the system into controlled oscillation.
Hagglund et al. disclosed a method of tuning a PID controller in U.S. Pat. No. 4,549,123, which is incorporated by reference. The method was an improvement over the Ziegler-Nichols method and allowed the tuning procedure to be performed automatically.
In the method disclosed by Hagglund et al., a non-linear circuit is provided in the controller feedback path in place of the PID controller. The circuit oscillates between amplitudes +d and -d based on changes in the process output signal y, thereby ensuring system oscillation.
The ultimate period T.sub.U is equal to the period of oscillation of the process output signal y, and the ultimate gain K.sub.U is calculated in accordance with the equation: ##EQU1## where d represents the amplitude of the output of the non-linear circuit and A.sub.T represents the amplitude of the process output signal y. Once the ultimate gain and period are determined, the PID controller parameters are calculated as discussed above. This method is known generally in the art as relay auto tuning.
Since the method disclosed by Hagglund et al. causes the system to quickly and consistently enter oscillation, and the controller parameters are easily calculated from measuring the period and amplitude of oscillation, the method may be performed automatically by the controller. However, the method can interfere with the normal operation of the controller. Therefore, as suggested by Hagglund et al., the method should only be executed occasionally.
More recently, progress has been made in defining optimal PID controller settings. For example, internal model control-based tuning rules (IMC) have been instituted and have gained recognition. However, in order to apply the IMC rules, a mathematical model of the process under control is required. Unfortunately, the Ziegler-Nichols method and the auto relay tuning method do not assume a specific process model and do not provide sufficient data to generate such a mathematical model.
This problem is addressed in U.S. Pat. No. 4,768,143 to Lane et al., which discloses an adaptive gain scheduling algorithm that uses a parameter estimation module that implements a recursive least squares algorithm. This patent is incorporated herein by reference. The process model disclosed in this patent is simplified to the first order without accounting for time delay and only provides for controller gain correction.
Significant improvement to this approach is disclosed in U.S. Pat. No. 4,882,526 to Iino et al., which is incorporated herein by reference. This patent discloses a time domain process model that is identified by using the auto-regressive moving average model (ARMA) and least squares method. From the time domain process model, the frequency characteristics of the process are obtained through model transformation. Controller parameters are then calculated to get a desired response based on the identified model. The disadvantages of this method are that it requires complex computation to get a time domain model and then transform this model to a frequency domain model, that it is unable to cope with changing process time delay, and that there is a need to inject a disturbance into the process to perform identification and tuning. The tuning process has to be initiated by the user.
In a paper by Balchen and Lie entitled An Adaptive Controller Based Upon Continuous Estimation Of The Closed Loop Frequency Response, Modeling, Identification and Control, Volume 8, No. 4, pages 223-240 (1987), direct computation in the frequency domain is used to cause an injected test frequency to converge on the ultimate frequency. An excitation signal derived from a sine wave signal at the test frequency is injected into the system set point signal, and the process control signal is applied to a frequency multiplier along with a mixing signal that is derived from a cosine wave signal having the same test frequency. The frequency multiplier produces a multiplier output signal, and the test frequency is slowly adjusted based on the multiplier output signal using a trial and error method until the test frequency is approximately equal to the ultimate frequency. The system is simple, however it does require that the excitation signal be injected into the set point signal, and convergence of the test signal is relatively slow.
Another method of self-tuning a process controller was disclosed in U.S. Pat. No. 4,855,674 to Murate et al. This method adjusts the controller parameters by observing oscillations in the process output signal. However, this method is only appropriate for underdamped processes. It is not appropriate for overdamped or critically damped processes that do not develop oscillations.